To improve the method, the PMFG graph is proposed [1]}.
The solution generates a graph embedded on a surface with a particular genus \(g\) . The genus of a surface is the number of holes in the surface, and \(g=0\)  corresponds to a topological sphere, \(g=1\)  to a torus, \(g=2\)  to
a double torus, etc.
The PMFG algorithm is generally the same as the MST one, except for the step \((3)\) .
It is replaced by the condition that the resulting graph should be embeddable on a surface with genus \(g\) .
The graph generated by the PMFG algorithm is a triangulation of the surface, and it contains \(3N+6g-6\)  links, which maximize the sum of \(C_{ij}\) .
The simplest case is the graph with \(g=0\) . In some sense, the PMFG graph could be viewed as the minimum extension towards the complexity after the MST tree.
